## New Online Math Game – Continuum

January 31st, 2011 by Math Tricks | No Comments | Filed in Fractals, Games, Golden Rectangle, Math Games, Math Geometry, Math Software, online math games

``` <!-- google_ad_client = "ca-pub-2176115693811858"; /* New Online Math Game - Continuum */ google_ad_slot = "7534657596"; google_ad_width = 468; google_ad_height = 60; //--> ```

## Continuum – Action Math Game!

The new online math game is out, and I hope you will enjoy it!

For this game, I included several math aspects.  The most obvious one is the use of fractals for the backgrounds.  I think they add a level of depth to the play fields – and are really cool to look at!

Next, I made all the bricks in the game golden rectangles.  Well, as close as I could anyway, because I had to use integer units in the design.  The dimensions of the bricks are 41 x 25 pixels, giving a ratio of 1.64 width to height, which is just a tad more than the actual value of approximately 1.61803399.

Lastly, I made as targets in the game polygons, which contain interfering balls after the polygons are destroyed.

This game is a little more mainstream from the others I have made for Math Tricks, but I think it is the most enjoyable.  Here is a game-play screen shot:

Anyway, it is online, and you can play it here.  Please feel free to give me any comments and suggestions!

## Golden Rectangle Dimensions

November 12th, 2009 by Math Tricks | No Comments | Filed in Golden Rectangle, Mathematics Concepts

``` <!-- google_ad_client = "ca-pub-2176115693811858"; /* Golden Rectangle Dimensions */ google_ad_slot = "0125204932"; google_ad_width = 468; google_ad_height = 60; //--> ```

So you have a single line of length X, and you want to extent the line to height Y such that you produce a golden rectangle.  Simple as pi pie!

This problem can be solved with some simple algebra, and it is useful if you wish to draw a golden rectangle given a line of any length.  For instance, you may want to incorporate golden rectangles into some artwork you are working on, or you may wish to crop photographs such that they are framed within a golden rectangle.

So, given a line of any length, you can break the line into two parts:

It is easy to see that:

From this, you can calculate that the length (A) of the sides of the square part of the golden rectangle is:

A = (A + B)/1.618

So just extend the line into a rectangle with base=(A+B) and height=(A+B)/1.618

Using this type of reasoning, if you have a square with a side of length A, and wished to extend the length to A+B such that the A+B is the length of the base of a golden rectangle, you can determine the length of B very easily: